Large losses and equilibrium in insurance markets

Abstract

We show that if losses are larger than wealth, then individuals with the option of declaring bankruptcy will not insure if the loss probability is above a threshold. In an insurance market with adverse selection, if the high risks’ loss probability is above the threshold, then no trade occurs at the Rothschild–Stiglitz equilibrium. Active trade in insurance requires cross-subsidization. When a subset of individuals with significant costs of bankruptcy and default is included in the market, then the equilibrium outcome always involves positive levels of insurance coverage for some individuals, but the parameters of the model determine whether all types receive coverage, or whether null contracts are received by both high and low risks with no bankruptcy costs or just the low risks from that group.

abstract = "We show that if losses are larger than wealth, then individuals with the option of declaring bankruptcy will not insure if the loss probability is above a threshold. In an insurance market with adverse selection, if the high risks’ loss probability is above the threshold, then no trade occurs at the Rothschild–Stiglitz equilibrium. Active trade in insurance requires cross-subsidization. When a subset of individuals with significant costs of bankruptcy and default is included in the market, then the equilibrium outcome always involves positive levels of insurance coverage for some individuals, but the parameters of the model determine whether all types receive coverage, or whether null contracts are received by both high and low risks with no bankruptcy costs or just the low risks from that group.",

N2 - We show that if losses are larger than wealth, then individuals with the option of declaring bankruptcy will not insure if the loss probability is above a threshold. In an insurance market with adverse selection, if the high risks’ loss probability is above the threshold, then no trade occurs at the Rothschild–Stiglitz equilibrium. Active trade in insurance requires cross-subsidization. When a subset of individuals with significant costs of bankruptcy and default is included in the market, then the equilibrium outcome always involves positive levels of insurance coverage for some individuals, but the parameters of the model determine whether all types receive coverage, or whether null contracts are received by both high and low risks with no bankruptcy costs or just the low risks from that group.

AB - We show that if losses are larger than wealth, then individuals with the option of declaring bankruptcy will not insure if the loss probability is above a threshold. In an insurance market with adverse selection, if the high risks’ loss probability is above the threshold, then no trade occurs at the Rothschild–Stiglitz equilibrium. Active trade in insurance requires cross-subsidization. When a subset of individuals with significant costs of bankruptcy and default is included in the market, then the equilibrium outcome always involves positive levels of insurance coverage for some individuals, but the parameters of the model determine whether all types receive coverage, or whether null contracts are received by both high and low risks with no bankruptcy costs or just the low risks from that group.